CN105717947A - Method for controlling an aerial apparatus, and aerial apparatus with controller implementing this method - Google Patents

Abstract

Method for controlling an aerial apparatus with a telescopic boom, strain gauge sensors for detecting the bending state of the telescopic boom in a horizontal and a vertical direction, a gyroscope attached to the top of the telescopic boom and control means for controlling a movement of the aerial apparatus on the basis of signal values gained from the SG sensors and the gyroscope, said method comprising the following steps: obtaining raw signals SGRaw, GYRaw from the SG sensors and the gyroscope, calculating reference signals from the raw signals SGRaw, GYRaw, including an SG reference signal SGRef, representing a strain value, and a gyroscope reference signal GYRef, representing an angular velocity value, and an angular acceleration reference signal AARef derived from angular position or angular velocity measurement values, reconstructing a first oscillation mode f1 and at least one second oscillation mode f2 from the reference signals and additional model parameters PAR related to the construction of the aerial apparatus, calculating a compensation angular velocity value AVComp from the reconstructed first oscillation mode f1 and at least one second oscillation mode f2, and adding the calculated compensation angular velocity value AVComp to a feedforward angular velocity value to result in a drive control signal.

Description

Control the method for aerospace equipment and have the aerospace equipment of the controller realizing the method

Technical field

The present invention relates to the method controlling aerospace equipment and the aerospace equipment of controller including realizing this control method.

Background technology

This aerospace equipment is the turntable ladder such as with flexible articulated jib (bendablearticulatedarm), and this flexible articulated jib is attached to the upper end of telescopic tube (telescopicboom).But, the invention is not restricted to this fire-fighting rack, but also include similar system, for instance, hinged or flexible platform and air rescue equipment.Generally, these systems are arranged on vehicle so that these systems are rotatable and can be upright.

Such as, according to file DE9416367U1, articulated jib is attached to the top of the top element of telescopic tube and highlights from the telescopic tube being fully retracted so that articulated jib can be rotatable at any time, and unrelated with the current extension elongation of sleeve pipe.The example of the ladder with the articulated jib that itself can stretch is open by EP1726733B1.In another alternative design, as disclosed in EP2182164B1, articulated jib is included in the top element of telescopic tube so that articulated jib can be fully retracted in telescopic tube, but rotatable from the length-specific on top.

Additionally, for the control device of turntable ladder, scaoffold etc. disclosed in EP1138868B1 and EP1138867B1.That discusses in these files common problem encountered is that during ladder movement the suppression vibrated.Along with the increase of ladder length, this problem even becomes more important.Therefore it has already been proposed that the sensor being used for detecting current vibration motion is attached at diverse location along telescopic tube.For this, employ strain-gage pickup (hereinafter also referred to as SG sensor (using SG as the abbreviation of " strain (straingauge) ")) and be attached at the top of telescopic tube, for directly measuring two axles added or three-axis gyroscope, this gyroscope fulcrum preferably close to articulated jib or the tip close to ladder of the angular velocity of the upper end of ladder.Provide the controller of the motion controlling aerospace equipment based on the signal value obtained from SG sensor and gyroscope.During operation, when being passed to controller particularly in the input order for moving aerospace equipment, by means of processing signal value, current vibration state is taken into account, the motion making ladder can be corrected, making the resilient flexibility regardless of sleeve pipe, the top of ladder all reaches and keeps target location.

Existing method for the vibration of active suppression turntable ladder or the sleeve pipe of similar device is not suitable for or may not apply to relatively large articulated jib, i.e. have the ladder of articulated jib and especially maximum operational height more than 32m.For these ladders, owing to the length of its sleeve pipe is relevant to its cross section, it is necessary to consider the spatial relationship of material, therefore it is not suitable for fully describing the elastic vibration of this ladder based on the lumped parameter model that lumped mass is approximate.It addition, not only fundamental vibration, and secondary resonance (and being likely to the resonance of more high order) needs by active suppression, and needs to consider the change of the impact on articulated jib and especially pivot angle (pivotangle).It addition, except the ladder of maximum 32m, it is impossible to assuming that elastic bending in the horizontal direction is independent of each other with torsion.But, as described in detail later, all vibration modes are relevant to the rotation of the curved deflector including combining of turntable and torsional deflection.

The method for Active vibration suppression and track following of the basic bending vibration of the known consideration of EP1138868B1 each pitching rotating shaft (elevationandrotationaxis) recorded from the above.These methods are applicable only to reach 32mde ladder without articulated jib and maximum height, for this ladder, only need for each axle to consider fundamental vibration.From the known improved method for hinged ladder of EP1772588B1, wherein, lumped parameter model is used to be similar to the vibration of hinged ladder.This model includes three quality point being connected to each other via elastic straining element.Therefore, this model and the vibration suppression developed later control to identify the spatial distribution attribute of sleeve pipe, therefore do not include the combination of horizontal curvature and torsion in design.It addition, more the resonance of high order is not by active suppression, but it is counted as interference, and uses interference observer to be filtered out by these resonance.The method is used in the measured value of strain gauge (SG) sensor of the lower end of sleeve pipe or the hydraulic pressure of actuator to detect vibration.For bigger hinged ladder, these measured values are sensitive not with enough snr measurement secondary resonance to all ladder length and the position at articulated jib, and in the ladder that considers in the present patent application, especially necessary with enough snr measurement the second resonance in all ladder length and the position of articulated jib.

The Active vibration suppression of the space trend identifying sleeve pipe is would know that from EP2022749B1.Using the theoretical bending to sleeve pipe of the euler beam with constant parameter to be modeled, the rescue cage on the top of sleeve pipe is modeled as rigid body, this results in the special dynamic boundary condition of beam.Based on Infinite-dimensional model mode be similar to, according to the measured value of the SG sensor of the lower end at sleeve pipe and the inertia measurement value in upper end, for instance measure the gyroscope of the identical rotating shaft speed of rotation, rebuild once with secondary resonance.Then, vibration mode obtains according to the solution of Algebraic Equation set, and all by active suppression.In the second approach, it is proposed that based on once with second harmonic curvature movement amendment model interference observer, for this observer, it is assumed that use SG sensor only measure fundamental vibration.Using observer signal, only fundamental vibration is by active suppression.The method neither includes articulated jib also not included in the combination of bending and moment of torsion in horizontal direction.It addition, observer is it is not intended that the unlike signal amplitude of SG sensor and gyroscope.

Summary of the invention

Therefore, it is an object of the present invention to provide a kind of method for controlling this aerospace equipment above, the method to provide effective vibration suppression for aerospace equipment by the combination of the bending in consideration horizontal direction and torsion, the method can be applied similarly to suppress the vibration in vertical direction by less variation, and the vibration in vertical direction potentially includes articulated jib and is attached to the impact on two axles of the cage of end of articulated jib.

This purpose realizes by being used for controlling the method for aerospace equipment,

This control device includes

-telescopic tube,

-strain-gage pickup, it is for detecting telescopic tube case of bending in the horizontal direction and the vertical direction,

-gyroscope, it is attached to the top of telescopic tube, and

-controlling equipment, it controls the motion of aerospace equipment based on the signal value obtained from SG sensor and gyroscope,

The method comprises the following steps:

-obtain primary signal SG from SG sensor and gyroscope_RawAnd GY_Raw,

-according to primary signal SG_RawAnd GY_RawCalculating reference signal, described reference signal includes the SG reference signal SG representing strain value_RefWith the gyroscope reference signal GY representing magnitude of angular velocity_Ref, and calculate the angular acceleration reference signal AA being worth going out from angular position value or angular velocity measurement_Ref,

-reconstruct the first vibration mode f according to described reference signal and the additional model parameter PAR relevant with the structure of aerospace equipment₁With at least one the second vibration mode f than described first vibration mode higher order₂,

-according to the first vibration mode f reconstructed₁With at least one the second vibration mode f₂Calculate compensation magnitude of angular velocity AV_Comp,

-by computed compensation magnitude of angular velocity AV_CompIt is added to obtain drive control signal with feedforward magnitude of angular velocity.

In the method according to the invention, it is thus achieved that from the signal of SG sensor and gyroscope as primary signal.Below, reference signal is calculated according to these primary signals.These reference signals include the SG reference signal relevant to SG sensor and gyroscope reference signal.SG reference signal represent Angle Position with elastic deflection for signal, and gyroscope reference signal represents magnitude of angular velocity, and each reference signal is used for corresponding spatial axes.

According to these reference signals and the additional model parameter relevant to the CONSTRUCTED SPECIFICATION of aerospace equipment, the vibration mode of requirement is reconstructed and for calculating compensation magnitude of angular velocity.In the preferred implementation, the first vibration mode and the second vibration mode are reconstructed.Computed compensation magnitude of angular velocity is superimposed on feedforward magnitude of angular velocity to obtain may be used for such as controlling hydraulically powered drive control signal.

In the dynamic mode of implicit the method, it is possible to separate the fundamental vibration of ladder from harmonic wave (overtone).It addition, the angular acceleration of each axle can calculate based on angular position measurement value, and it is fed to the dynamic model of ladder with the caused vibration of the motion predicting each axle.The vibration signal estimated is used for calculating approximation control signal to suppress these to vibrate.This control signal is superimposed upon on the motion command of needs, it is necessary to motion command represented by the magnitude of angular velocity that feedovers, determine based on the reference signal read from the manual lever that operated by human operator who, or carried out order by path following control.Based on reference signal, the calculating of motion command needed it is designed to provide smooth reaction and reduces the excitation of the vibration to ladder.The drive control signal obtained is transferred to for controlling the actuator of driving device being associated with each axle.This principle may be used for raise/lower (elevation/depression) and is used for rotating (turntable) axle.For raising, all vibration modes include pure bending, and for rotating, all vibration modes are the bending vibration and twisting vibration that combine.

Preferred embodiment according to the method according to the present invention, the difference of the primary signal that calculating SG reference signal includes the SG sensor of the meansigma methods of the primary signal of the SG sensor according to the vertical curve measuring telescopic tube or the horizontal curvature of measurement telescopic tube calculates strain value, and this strain value is carried out high-pass filtering.Filtering helps compensate for the biasing of signal.

According to another preferred embodiment of the method, calculate SG reference signal also to include: insert (interpolate) strain-bias value according to the extension elongation of the angle of pitch of telescopic tube and telescopic tube, correct this strain value by deducting strain-bias value from strain value before high-pass filtering.The calculating of strain-bias value compensate for the impact of gravity.

According to another preferred embodiment, insertion strain-bias is additionally based upon the extension elongation of the articulated jib of the end being attached to telescopic tube and the inclination angle between telescopic tube and articulated jib.

According to another preferred embodiment, insert strain-bias value and be additionally based upon the end being attached to telescopic tube or be attached to the load in the quality of cage of end of articulated jib and cage.

Another preferred embodiment according to the method, computing gyroscope reference signal includes: calculate the backward difference quotient of primary signal respectively according to the angular position measurement value of the angle of pitch and the anglec of rotation to obtain Attitude rate estimator signal, estimated that signal is filtered by low pass filter angular velocity, calculate the particular of the filtered Attitude rate estimator signal being associated with each axle of gyroscope, this part of filtered Attitude rate estimator signal is deducted from the initial primary signal from gyroscope, to obtain compensated gyroscope signal, compensated gyroscope signal is carried out low-pass filtering.This is the component in order to cause from the rudimentary horn VELOCITY EXTRACTION of measured gyroscope by elastic vibration.

Another embodiment according to the method according to the present invention, calculating compensation magnitude of angular velocity includes reference position control component and is added with the signal value calculated according to the first reconstructed vibration mode and the second vibration mode, and this reference position control component relates to current location and deviates from the deviation of reference position.

According to another embodiment, feedforward magnitude of angular velocity obtains from the trajectory planning assembly calculating reference angular velocities signal based on original input signal, and dynamic vibration eliminates assembly amendment reference angular velocities signal to reduce the excitation to vibration.

The invention still further relates to aerospace equipment, including telescopic tube, for detecting strain gauge (SG) sensor of the strain-gage pickup of telescopic tube case of bending in the horizontal direction and the vertical direction, it is attached to the gyroscope at the top of telescopic tube, and the controller of the motion of aerospace equipment is controlled based on the signal value obtained from SG sensor and gyroscope, wherein, control equipment realizes above-mentioned control method.

Preferred embodiment according to aerospace equipment, at least four SG sensor, with two pairs of layouts, the top of the cross section that every a pair is arranged in telescopic tube and lower curtate, makes two SG transducer arrangements opposite side at telescopic tube of every centering.In arranging at this, can be used for drawing the signal horizontally or vertically bent measuring telescopic tube at the bottom of telescopic tube and top or the different value of two SG sensors arranged with right side to the left respectively.

Another preferred embodiment according to this aerospace equipment, articulated jib is attached to the end of telescopic tube.

According to another preferred embodiment, the rescue cage of end that aerospace equipment also includes being attached to telescopic tube or the end that is attached to articulated jib.

Accompanying drawing explanation

The example of the preferred embodiments of the present invention is described in detail below with reference to drawings below.

Fig. 1 a and Fig. 1 b is the schematic diagram of the model of the aerospace equipment showing different model parameters in side view with top view；

Fig. 2 is the detailed view of the aerospace equipment of the rescue cage with the end being arranged on articulated jib showing alternate model parameter in side view；

Fig. 3 is the opposite side view of the according to an embodiment of the invention complete aerospace equipment of the position showing sensor；

Fig. 4 is the schematic diagram of the control system realized in the controller according to the aerospace equipment of the present invention；

Fig. 5 and Fig. 6 is the detailed maps of the parts of the control system illustrating Fig. 4, and they respectively show the calculating to SG reference signal and gyroscope reference signal；And

Fig. 7 is another detailed view of the control system of Fig. 4, which show the calculating compensating magnitude of angular velocity.

Detailed description of the invention

First, reference dynamic model is described the basis of the control method according to the present invention, Fig. 1 a, Fig. 1 b and Fig. 2 also be will be further referenced and describe this dynamic model.

The model being based on the properties of distributions considering material parameter for the method for Active vibration suppression as the theme of this patent application.When extensible canopy includes several element, for each element therein, main physical parameters approximately constant in the whole length of element, but generally distinguished from one another, and due to the overlap of two or more telescopic elements, the physical parameter of this model is each assumed to piecewise constant.Model based on these hypothesis occurs in " " VerteiltparametrischeModellierungundRegelungeiner60m-Feu erwehrdrehleiter "; byPertsch; A.andSawodny; O.; publishedinat-Automatisierungstechnik9 (September2012); pages522to533 " and at " " 2-DOFControlofaFire-RescueTurntableLadder ", byZimmert, the N. for pitch axis；Pertsch, A.undSawodny, O., publishedinIEEETrans.Contr.Sys.Technol.20.2 (March2012), pages438 452 " in and at " " ModelingofCoupledBendingandTorsionalOscillationsofanIncl inedAerialLadder ", byPertsch, A.undSawodny, O., publishedinProc.ofthe2013AmericanControlConference.Washi ngtonD.C., USA, 2013, pages4098-4103fortherotationaxis " in.It is modified to include articulated jib to elastic vibration and the impact on bending and the combination of moment of torsion from these models openly known.

In order to illustrate the method, the equation of motion of the combination including bending and moment of torsion of rotating shaft will be shown for.Figure 1 illustrates the model for describing these motions.Wherein w_k(x, t) and γ_k(x t) represents each elastic bending in the kth section in segmentation beam and torsion respectively；T express time and x represent the space coordinates of the shear centre axle along sleeve pipe；α and θ represents the angle of pitch and the anglec of rotation respectively；D_kRepresent the distance between shear centre axle and the mass axis of beam；μ_kAnd v_kRepresent inertia mass and the inertia mass square of per unit length respectively；Represent around z-axis bending area inertia moment andRepresent the torque coefficient in cross section；L represents the current length of the extension ladder measured from substrate to fulcrum；J_TRepresent the mass mement of inertia of turntable；M_TRepresent moment turntable used by hydraulic electric motor.Introduce the strain rate with rejection coefficient β to suppress, and wherein h_α(x)=xcos α-d_kSin α, the equation of motion in kth section is

${\mathrm{\μ}}_k\left({\stackrel{\·\·}{w}}_k\right(x,t)-d_k{\stackrel{\·\·}{\mathrm{\γ}}}_k(x,t)+h_{\mathrm{\α}}(x\left)\stackrel{\·\·}{\mathrm{\θ}}\right(t\left)\right)+{\mathrm{EI}}_k^z\left(w_k^{\′\′\′\′}\right(x,t)+\mathrm{\β}{\stackrel{\·}{w}}_k^{\′\′\′\′}(x,t\left)\right)=0---\left(1a\right)$

${\mathrm{\μ}}_k{d}_k\left({\stackrel{\·\·}{w}}_k\right(x,t)-d_k{\stackrel{\·\·}{\mathrm{\γ}}}_k(x,t)+h_{\mathrm{\α}}(x\left)\stackrel{\·\·}{\mathrm{\θ}}\right(t\left)\right)$

$-v_k\left({\stackrel{\·\·}{\mathrm{\γ}}}_k\right(x,t)+sin(\mathrm{\α}\left)\stackrel{\·\·}{\mathrm{\θ}}\right(t\left)\right)+{\mathrm{GI}}_k^t\left({\mathrm{\γ}}_k^{\′\′}\right(x,t)+\mathrm{\β}{\stackrel{\·}{\mathrm{\γ}}}_k^{\′\′}\left(t\right)=0---\left(1b\right)$

Wherein, upper punctuate represents the derivative relative to time t and the basic derivative (primederivative) relative to space coordinates x.Static boundary condition is given

w₁(0, t)=0, w '₁(0, t)=0, γ '₁(0, t)=0, (2)

Further, the condition of continuity of the deflection of the boundary between each two in portion P, power and moment, i.e. for k=2...P-1, be

$w_k(x_k^{-},t)=w_{k+1}(x_k^{+},t),w_k^{\′}(x_k^{-},t)=w_{k+1}^{\′}(x_k^{+},t),{\mathrm{\γ}}_k(x_k^{-},t)={\mathrm{\γ}}_{k+1}(x_k^{+},t)---\left(3a\right)$

${\mathrm{EI}}_k^z\left(w_k^{\′\′}\right(x_k^{-},t)+\mathrm{\β}{\stackrel{\·}{w}}_k^{\′\′}(x_k^{-},t\left)\right)={\mathrm{EI}}_{k+1}^z\left(w_{k+1}^{\′\′}\right(x_k^{+},t)+\mathrm{\β}{\stackrel{\·}{w}}_{k+1}^{\′\′}(x_k^{+},t\left)\right)---\left(3b\right)$

${\mathrm{EI}}_k^z\left(w_k^{\′\′\′}\right(x_k^{-},t)+\mathrm{\β}{\stackrel{\·}{w}}_k^{\′\′\′}(x_k^{-},t\left)\right)={\mathrm{EI}}_{k+1}^z\left(w_{k+1}^{\′\′\′}\right(x_k^{+},t)+\mathrm{\β}{\stackrel{\·}{w}}_{k+1}^{\′\′\′}(x_k^{+},t\left)\right)---\left(3c\right)$

${\mathrm{GI}}_k^p\left({\mathrm{\γ}}_k^{\′}\right(x_k^{-},t)+\mathrm{\β}{\stackrel{\·}{\mathrm{\γ}}}_k^{\′}(x_k^{-},t\left)\right)={\mathrm{GI}}_{k+1}^p\left({\mathrm{\γ}}_k^{\′}\right(x_k^{+},t)+\mathrm{\β}{\stackrel{\·}{\mathrm{\γ}}}_k^{\′}(x_k^{+},t\left)\right)---\left(3d\right)$

When respectively from left side (x < x_k) and right side (x > x_k) close to x_kTime, function parameterWithIt is introduced into, as the simplification symbol of the ultimate value of respective function.The impact of the cage being all modeled as on the articulated jib of rigid body and beam is included in a model via dynamic boundary condition.Position and the orientation of these entities depend on pivot angleAnd owing to the horizontal leveling of cage additionally depends on lift angle (raisingangle).To put it more simply, following merely illustrate the impact of (change) the synthesis center of gravity of cage and the articulated jib including payload.When including the mass mement of inertia of articulated jib and cage, obtain the similar equation of this model.Position of centre of gravity depends primarily on pivot angleThe extension elongation L of articulated jib_AAWith payload mass m_p.As shown in fig 2, the gross mass of articulated jib, cage and payload be modeled as be positioned at a distance of pivot distance be r (L_AA, m_p) particle.It is abbreviated asWithThen it is given at the boundary condition at x=L place

$\begin{array}{c}m\mathrm{\&eta;}\left({\stackrel{\&CenterDot;\&CenterDot;}{w}}_P\right(L)+\mathrm{\&xi;}{\stackrel{\&CenterDot;\&CenterDot;}{w}}_P^{\&prime;}\left(L\right)-\mathrm{\&eta;}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&gamma;}}}_P\left(L\right))-{\mathrm{GI}}_P^t\left({\mathrm{\&gamma;}}_P^{\&prime;}\right(L)+\mathrm{\&beta;}{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}_P^{\&prime;}\left(L\right))\\ =-m\mathrm{\&eta;}\left(\right(L+\mathrm{\&xi;})\cos \mathrm{\&alpha;}-\mathrm{\&mu;}\sin \mathrm{\&alpha;})\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}\end{array}---\left(4a\right)$

$\begin{array}{c}-m\left({\stackrel{\&CenterDot;\&CenterDot;}{w}}_P\right(L)+\mathrm{\&xi;}{\stackrel{\&CenterDot;\&CenterDot;}{w}}_P^{\&prime;}\left(L\right)-\mathrm{\&eta;}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&gamma;}}}_P\left(L\right))+{\mathrm{EI}}_P^z\left(w_P^{\&prime;\&prime;\&prime;}\right(L)+\mathrm{\&beta;}{\stackrel{\&CenterDot;}{w}}_P^{\&prime;\&prime;\&prime;}\left(L\right))\\ =m\left(\right(L+\mathrm{\&xi;})\cos \mathrm{\&alpha;}-\mathrm{\&eta;}\sin \mathrm{\&alpha;})\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}\end{array}---\left(4b\right)$

$\begin{array}{c}-m\mathrm{\&xi;}\left({\stackrel{\&CenterDot;\&CenterDot;}{w}}_P\right(L)+\mathrm{\&xi;}{\stackrel{\&CenterDot;\&CenterDot;}{w}}_P^{\&prime;}\left(L\right)-\mathrm{\&eta;}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&gamma;}}}_P\left(L\right))-{\mathrm{EI}}_P^z\left(w_P^{\&prime;\&prime;}\right(L)+\mathrm{\&beta;}{\stackrel{\&CenterDot;}{w}}_P^{\&prime;\&prime;}\left(L\right))\\ =m\mathrm{\&xi;}\left(\right(L+\mathrm{\&xi;}))\cos \mathrm{\&alpha;}-\mathrm{\&eta;}sin\mathrm{\&alpha;})\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}\end{array}---\left(4c\right)$

The sports immunology of turntable is

$J_T\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}\left(t\right)-cos\mathrm{\&alpha;}\left({\mathrm{EI}}_1^z\right(w_1^{\&prime;\&prime;}\left(0,t\right)+\mathrm{\&beta;}{\stackrel{\&CenterDot;}{w}}_1^{\&prime;\&prime;}\left(0,t\right)\left)\right)$

$-\sin \mathrm{\&alpha;}\left({\mathrm{GI}}_1^t\right({\mathrm{\&gamma;}}_1^{\&prime;}\left(0,t\right)+\mathrm{\&beta;}{\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}}^{\&prime;}\left(0,t\right)\left)\right)=M_T---\left(5\right)$

By selecting following formula the time in (1) and spatial dependence to be separated

w_k(x, t)=W_k(x)e^jωt, γ_k(x, t)=Γ_k(x)e^jωt, (6)

Wherein, j is illusion unit, free in kth section (unrestraint and unforced, i.e. β=0,) characteristic equation of eigenfunction of problem is

$(\frac{{\&part;}^6}{\&part;x^6}+(v_k+{\mathrm{\&mu;}}_k{d}_k^2)\frac{{\mathrm{\&omega;}}^2}{{\mathrm{GI}}_k^t}\frac{{\&part;}^4}{\&part;x^4}-\frac{{\mathrm{\&omega;}}^2{\mathrm{\&mu;}}_k}{{\mathrm{EI}}_k^z}\frac{{\&part;}^2}{\&part;x^2}-\frac{{\mathrm{\&omega;}}^2{v}_k}{{\mathrm{GI}}_k^t}\frac{{\mathrm{\&omega;}}^2{\mathrm{\&mu;}}_k}{{\mathrm{EI}}_k^z})W_k\left(x\right)=0---\left(7\right)$

Followed by with Γ_kX () replaces W_kThe same characteristic features equation of (x).ω represents the intrinsic angular frequency of corresponding eigen mode.The solution of spatial differential equation (7) is given eigenfunction

W_k(x)=A_1ksinh(s_1kx)+A_2kcosh(s_1kx)+A_3ksin(s_2kx)

-A_4kcos(s_2kx)+A_5ksin(s_3kx)+A_6kcos(s_3kx)(8a)

Γ_k(x)=B_1ksinh(s_1kx)+B_2kcosh(s_1kx)+B_3ksin(s_2kx)

+B_4kcos(s_2kx)+B_5ksin(s_3kx)+B_6kcos(s_3kx)(8b)

By eigenfunction (8) being substituted into together with (6) equation of motion (1) and using the foregoing simplification obtained from the hypothesis of the motion of freedom, unrestraint and unforced to obtain correlation coefficient A_nkWith B_nkBetween relation.Use these relations, it is possible to obtain coefficient S respectively by the identical hypothesis made before (8) being substituted into the equation obtained with the condition of continuity (2)-(4) according to boundary condition and applying_nk、A_nkAnd B_nk(until convergent-divergent constant) and eigenfrequency ω.Then, these coefficients follow the nontrivial solution of the equation group obtained.

Below, remember the segmentation definition of W (x) and Γ (x), remove space factor k.Eigenvalue problem has infinite multiple solution, and these solutions are for belonging to i-th eigenfrequency ω_iEigen[value should be expressed as Wⁱ(x) and Γⁱ(x).Use series expression

$w(x,t)={\mathrm{\&Sigma;}}_{i=1}^{\mathrm{\&infin;}}{W}^i\left(x\right)f_i\left(t\right),\mathrm{\&gamma;}(x,t)={\mathrm{\&Sigma;}}_{i=1}^{\mathrm{\&infin;}}{\mathrm{\&Gamma;}}^i\left(x\right)f_i\left(t\right)$

Wherein, f_iThe evolution in time of the amplitude of (t) description i-th eigenfunction, and this series is represented the substitution equation of motion, and substitute into boundary condition and the condition of continuity, it is possible to obtain following ordinary differential equation for each model:

$\begin{array}{c}{a}_i\left({\stackrel{\&CenterDot;\&CenterDot;}{f}}_i\right(t)+{\mathrm{\&beta;\&omega;}}_i{\stackrel{\&CenterDot;}{f}}_i\left(t\right)+{\mathrm{\&omega;}}_i^2{f}_i\left(t\right))=(\frac{{\mathrm{GI}}_1^t}{{\mathrm{\&omega;}}_i^2}{\left({\mathrm{\&Gamma;}}^i\right)}^{\&prime;}{|}_{x=0}sin\mathrm{\&alpha;}+\frac{{\mathrm{EI}}_1^z}{{\mathrm{\&omega;}}_i^2}{\left(W^i\right)}^{\&prime;\&prime;}{|}_{x=0}cos\mathrm{\&alpha;})\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}\left(t\right)\\ i=1...\mathrm{\&infin;}\end{array},---\left(8\right)$

a_iIt is depending on the normaliztion constant of eigenfunction (not exclusive) convergent-divergent.Therefore, by selecting suitable convergent-divergent, a is supposed below_i=1.

By infinite equation group (9) foreshortens to the pattern of requirement, it is thus achieved that finite dimension mode represents, wherein, select to reach desired model accuracy to pattern quantity.Below, describing the Active vibration suppression for two resonance, Active vibration suppression is enough often due to more height mode and band-limited naturally suppression of actuator.It is simply and is extended including more node at Active vibration suppression.

The equation of motion of two patterns can be written as the equation below with sytem matrix A and input matrix B:

$\stackrel{\&CenterDot;}{x}=\left[\begin{array}{cccc}0& 1& & \\ -{\mathrm{\&omega;}}_1^2& -{\mathrm{\&beta;\&omega;}}_1& & \\ & & 0& 1\\ & & -{\mathrm{\&omega;}}_2^2& -{\mathrm{\&beta;\&omega;}}_2\end{array}\right]x+\left[\begin{array}{cc}0& 0\\ b_1^s& b_1^c\\ 0& 0\\ b_2^s& b_2^c\end{array}\right]\left[\begin{array}{c}sin\mathrm{\&alpha;}\\ cos\mathrm{\&alpha;}\end{array}\right]\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}=Ax+B\left(\mathrm{\&alpha;}\right)\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}---\left(10\right)$

Right according to (9)WithDefinition be obvious.

Compensate turntable dynamically (5) by inner control loop, it also offers the setting point tracking of the required angular velocity that turntable rotates.If this control loop is sufficiently fast compared to characteristic value, then actuator dynamically (5) can be approximated to be first-order lag

$\mathrm{\&tau;}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}+\stackrel{\&CenterDot;}{\mathrm{\&theta;}}=u.---\left(11\right)$

If time delay, constant, τ was sufficiently small, then input can directly be counted as speed reference inputTherefore, the angular acceleration in (10) can be usedReplace.Based on model, (10) are described, the control feedback signal u of Active vibration suppression_fbFollowing state feedback law is used to obtain

$u_{fb}=-\left[\begin{array}{cccc}{k}_1^p& k_1^d& k_2^p& k_2^d\end{array}\right]x---\left(12\right)$

Realize required dynamic behaviour by suitably selecting feedback oscillator, closed-loop pole can be set to and be specifically arranged to increase the level suppressed.Pivot angle based on lift angle α, articulated jibAnd the length L of the length L of ladder and articulated jib_AARegulate gainWithIf turntable dynamic internal control ring is sufficiently fast, i.e. input is seen as the reference of rotary speed, then partial state feedback is enough to increase suppression, wherein,

$u_{fb}=-\left[\begin{array}{cccc}{k}_1^p& 0& k_2^p& 0\end{array}\right]x.---\left(13\right)$

In order to realize whole state feedback law or partial state feedback rule, it must be understood that state vector.In the preferred implementation, whole state observers are used for determining state vector.In alternative realization, provide the partial reconfiguration of state vector, as the solution of Algebraic Equation set, wherein, extend to the bending-twisting vibration of combination from the EP2022749 method known.For any method, it is all necessary for measuring vibration.Technically feasible scheme includes the hydraulic pressure measuring actuator, uses strain gauge to measure the surface strain of sleeve pipe, and such as uses accelerometer or gyroscope to measure inertia.Alternatively, except except the strain gauge of side, it is also possible to use the measured value to angular speed (that is, around the axle being perpendicular to sleeve pipe) on bending direction or be attached to the top side of sleeve pipe or the measured value of the strain gauge of bottom side.In order to make such as by vertical curve cause minimizing twisting, be used in the difference between the strain gauge on both sides, as horizontal curvature, owing to the position of strain gauge is at the opposite side of beam, so two signal intensities are in opposite direction.In preferred disposition, wherein, at x=x_SG(their difference is expressed as ε_h) place strain gauge and at x=x_GYThe angular velocity of rotation of what the gyroscope measurement at place was lingered longitudinal axis, the measurement equation of this state space system is

$\begin{array}{c}y=\left[\begin{array}{c}{\mathrm{\&epsiv;}}_h\\ m_T\end{array}\right]=\left[\begin{array}{cccc}\mathrm{\&zeta;}{\left(W^1\right)}^{\&prime;\&prime;}\left(x_{SG}\right)& 0& \mathrm{\&zeta;}{\left(W^2\right)}^{\&prime;\&prime;}\left(x_{SG}\right)& 0\\ 0& {\mathrm{\&Gamma;}}^1\left(x_{Gy}\right)& 0& {\mathrm{\&Gamma;}}^2\left(x_{Gy}\right)\end{array}\right]x+\left[\begin{array}{c}0\\ -\sin \mathrm{\&alpha;}\end{array}\right]\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\\ =Cx+D\left(\mathrm{\&alpha;}\right)\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\end{array}---\left(14\right)$

Wherein, ζ is the strain gauge distance to neutrality (without the strain) axle of horizontal curvature.It is alternatively possible to use the measured value of the angular velocity of the rotation of the opposing connection axle vertical with the top surface of beam or basal surface, from x=x_GYThe gyroscope at place obtains this measured value (signal m_R), obtain measuring equation

$y=\left[\begin{array}{c}{\mathrm{\&epsiv;}}_h\\ m_R\end{array}\right]=\left[\begin{array}{cccc}\mathrm{\&zeta;}{\left(W^1\right)}^{\&prime;\&prime;}\left(x_{SG}\right)& 0& \mathrm{\&zeta;}{\left(W^2\right)}^{\&prime;\&prime;}\left(x_{SG}\right)& 0\\ 0& {\left(W^1\right)}^{\&prime;}\left(x_{Gy}\right)& 0& {\left(W^2\right)}^{\&prime;}\left(x_{Gy}\right)\end{array}\right]x+\left[\begin{array}{c}0\\ cos\mathrm{\&alpha;}\end{array}\right]\stackrel{\&CenterDot;}{\mathrm{\&theta;}}.$

To put it more simply, hereinafter only consider the measurement equation provided in (14).The more convenient expression of output matrix C is obtained by zoom state vector x.In order to represent system with " gyroscope coordinate ", can will convertApplication and sytem matrix (10) and output matrix (14), wherein, provide T as nonsingular diagonal transformation matrix

T=diag ([Γ¹(x_Gy), Γ¹(x_Gy), Γ²(x_Gy), Γ²(x_Gy)])。

The transformation system equation obtained is

$\stackrel{\&CenterDot;}{\tilde{x}}={\mathrm{TAT}}^{-1}\tilde{x}+TB\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}},y={\mathrm{CT}}^{-1}\tilde{x}+D\left(\mathrm{\&alpha;}\right)\stackrel{\&CenterDot;}{\mathrm{\&theta;}}---\left(15\right)$

When conversion is corresponding to during to the pure convergent-divergent of state variable, under this conversion, sytem matrix is constant, i.e. TAT^-1=A.But, output matrix is normalized so that all non-zero records in a second row corresponding with the measured value of gyroscope are unified,

$y={\mathrm{CT}}^{-1}=\left[\begin{array}{cccc}{c}_1& 0& c_2& 0\\ 0& 1& 0& 1\end{array}\right]x+\left[\begin{array}{c}0\\ -\sin \mathrm{\&alpha;}\end{array}\right]\stackrel{\&CenterDot;}{\mathrm{\&theta;}}---\left(16\right)$

Similarly, state space system also is able to be converted into " strain coordinate ", and for this " strain coordinate ", the respective record in the first row of output matrix is unified, and record in a second row is change.It is likely to and the two is combined, for instance, for below equation, represent first mode with " strain coordinate ", and represent the second pattern with " gyroscope coordinate ",

$y=\left[\begin{array}{cccc}{c}_1& 0& 1& 0\\ 0& 1& 0& g_2\end{array}\right]x+\left[\begin{array}{c}0\\ -\sin \mathrm{\&alpha;}\end{array}\right]\stackrel{\&CenterDot;}{\mathrm{\&theta;}}---\left(17\right)$

All these normalization represent this have the advantage that to determine during operation, the quantity of systematic parameter that stores and to adjust is minimized.As the improvement compared with EP2022749B2, the system description in (14) considers strain gauge and also measures second harmonic vibration, and it is different with the amplitude of gyroscope measured value to consider strain gauge measured value.Equation group (10) and all parameters of output equation (16), (17) can be identified respectively via suitable modal identification algorithm according to experimental data.

In order to reconstruct elastic vibration according to measured value, first, deduct, from measured gyroscope signal, the rigid body rotation that the rotation rotated by turntable causes.The angular velocity of each axle can obtain respectively through the numerical differentiation of lift angle α and the measured value of rotation angle θ, and these measured values can such as be provided by incremental encoder or absolute value encoder.Alternatively, the additional gyroscope of the bases not suffering from the ladder of elastic vibration can be used for obtaining angular velocity.In the second step, all it is filtered strain gauge signal and compensated gyroscope signal reducing quiescent biasing and measuring the noise impact on signal, thus selecting filter frequencies in the distance that the essential frequency from system is suitable, thus not making distorted signals.Below, compensated and filtered signal is expressed as

In the preferred implementation, Luenberger observer is designed based on the system representation with calculation matrix (17).As shown in (15), apply suitable coordinate transform, in (10), provide sytem matrixAnd obtain input matrix according to (10)Make output matrixIt it is the form of the first matrix in (17).Observer state vector

$\hat{x}={\&lsqb;f_1,{\stackrel{\&CenterDot;}{f}}_1,f_2,{\stackrel{\&CenterDot;}{f}}_2,{\mathrm{\&epsiv;}}^{off},m^{off}\&rsqb;}^t---\left(18\right)$

Increase along with the bias state of each strain gauge and gyroscope, so that biasing remaining after filtering is taken into account.Observer equation is given

$\stackrel{\&CenterDot;}{\hat{x}}=\hat{A}\hat{x}+\hat{B}\left(\mathrm{\&alpha;}\right)\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&OverBar;}{\mathrm{\&theta;}}}+L(\tilde{y}-C\hat{x})---\left(19\right)$

Key element by appropriately selected observer gain matrix L, it is possible to the convergence rate of adjustment observer and Disturbance Rejection are to realize desired behavior.Angular accelerationEstimation can be obtained by the numerical differentiation of turntable speed estimated, suppress measured value and quantizing noise to increase by suitably filtering.Obviously include the vibrational excitation of angular acceleration by turntable due to state observer, these vibrations are predicted in some sense, which improve the response time of Active vibration suppression.The state estimation obtained from observer realizes state feedback law (12), (13) respectively for realization.Estimation preferably gyroscope coordinate to the first mode being in " strain coordinate " because the relation between the direction of turntable acceleration and the bending obtained will not reindexing (sign), unrelated with pivot angle, with vibration torque component contrary.By contrast, secondary resonance needs to estimate according to gyroscope measured value, because these vibrations are limited primarily to the top of telescopic tube, and owing to towards the size of based increase and bending stiffness, in strain gauge signal, the amplitude of these vibrations is relatively low.

In alternative realization, as from EP2022749B2 it can be seen that directly obtain the eigen mode solution as system of linear equations.Use the system representation obtained for the vibration combined, it is possible to apply method given in this article.Gyroscope signal that is compensated and that filterAccumulate in time, then obtain being estimated as eigen mode

$\left[\begin{array}{c}{\hat{f}}_1\\ {\hat{f}}_2\end{array}\right]={\left[\begin{array}{cc}{c}_1& 1\\ 1& g_3\end{array}\right]}^{-1}\left[\begin{array}{c}{\widetilde{\mathrm{\&epsiv;}}}_h\\ {\&Integral;}_0^t{\tilde{m}}_T\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}\end{array}\right]---\left(20\right)$

If c₁g₂≠ 1, it is possible to have the inverse of output matrix.In order to increase the robustness of anti-model uncertainty and in order to improve separation, the eigen mode of estimation also needs to be filtered.For the method, the quantity of measured value is necessarily equal to the quantity of the eigen mode to reconstruct, and therefore, extending to the bigger pattern of quantity needs additional sensor.In order to use axis of gyroscope m in (20)_RReplace m_T, it is necessary to suitably select coefficient c₁And g₂。

For pitch axis, but not for rotating shaft, it is not necessary to consider that any combination affects, and eigen mode can be modeled as pure bending.Bending in vertical direction is expressed as v_k(x, t), the equation of motion

${\mathrm{\&mu;}}_k\left({\stackrel{\&CenterDot;\&CenterDot;}{v}}_k\right(x,t)+x\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}(t\left)\right)+{\mathrm{EI}}_k^y\left(v_k^{\&prime;\&prime;\&prime;\&prime;}\right(x,t)+\mathrm{\&beta;}{\stackrel{\&CenterDot;}{v}}_k^{\&prime;\&prime;\&prime;\&prime;}(x,t\left)\right)=0---\left(21\right)$

Except without the concern for torsional deflection (γ_kOutside (x, t) ≡ 0), it is similar to first equation of motion of rotating shaft (1a).The impact of gravity mainly causes static deflection, and static deflection does not affect the elastic movement about balance, and is therefore not included in dynamic model.Additionally, the distance h in (1a)_αX () is replaced by the distance x of the longitudinal axis along sleeve pipe, and bending stiffness is replaced by the corresponding constant of the bending around z-axis.Note, it is suppressed that factor beta relates to the bending in vertical direction and its value is typically different than the value of horizontal curvature.When by v_kReplace w_kTime, boundary condition and the condition of continuity have (2) and (3) to provide, wherein, to for v_kCondition indifferent to.Equivalently, the boundary condition on top is by (4b, c) provides, wherein η=0, then substitutes into deflection and the bending strength of vertical axis.In order to simplify expression, do not repeat these equations.The similar process of the equation of motion about rotating shaft is caused the fourth order eigenvalue problem of free uninhibited movement, such as what such as summarize in cited before " " VerteiltparametrischeModellierung ... ", byPertschandSawodny ".Using the eigen[value obtained, elastic vibration can describe based on a series of expression

$v(x,t)={\mathrm{\&Sigma;}}_{i=1}^{\mathrm{\&infin;}}{V}^i\left(x\right)f_i\left(t\right)$

By to the suitable normalization of eigenfunction, being similar to (9), the time dependence f of each pattern_iT () is provided by the following equation being typically different:

$\left({\stackrel{\&CenterDot;\&CenterDot;}{f}}_i\right(t)+{\mathrm{\&beta;\&omega;}}_i{\stackrel{\&CenterDot;}{f}}_i(t)+{\mathrm{\&omega;}}_i^2{f}_i(t\left)\right)=\frac{{\mathrm{EI}}_1^y}{{\mathrm{\&omega;}}_i^2}{\left(V^i\right)}^{\&prime;\&prime;}{|}_{x=0}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}\left(t\right),i=1...\mathrm{\&infin;}---\left(22\right)$

Finite dimension for two patterns is similar to, and introduces state vectorAnd the equation of motion of first two pattern can be written as

$\stackrel{\&CenterDot;}{x}=\left[\begin{array}{cccc}0& 1& & \\ -{\mathrm{\&omega;}}_1^2& -{\mathrm{\&beta;\&omega;}}_1& & \\ & & 0& 1\\ & & -{\mathrm{\&omega;}}_2^2& -{\mathrm{\&beta;\&omega;}}_2\end{array}\right]x+\left[\begin{array}{c}0\\ b_1\\ 0\\ b_2\end{array}\right]\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}=Ax+B\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}---\left(23\right)$

Although the labelling method of pitch axis be chosen to substantially uniform with the labelling method of rotating shaft with simplify compare, but all variablees in (23) relate to vertical curve vibration and unrelated with the horizontal flexural vibration above considered.Using for the suitable convergent-divergent of state vector, the system output provided as the measured value of the strain gauge in bottom and the gyroscope on top can be written as

$y=\left[\begin{array}{cccc}{c}_1& 0& c_2& 0\\ 0& 1& 0& 1\end{array}\right]x+\left[\begin{array}{c}0\\ 1\end{array}\right]\stackrel{\&CenterDot;}{\mathrm{\&alpha;}}---\left(24\right)$

Based on this system description, use Luenberger observer can estimate whole state vector or the inverse estimating part state vector via the output matrix similar with (20), this is not being carried out detailed repetition.

Vibration suppressing method described above is introduced in vibration and considers vibration suppression afterwards.Except the method, use suitable feed forward control method can reduce during the proactive command of sleeve pipe is moved the excitation vibrated.Feed forward control method includes two major parts: trajectory planning assembly and dynamic vibration eliminate assembly.Trajectory planning assembly based on by human operator who via manual lever order or the original input signal that obtains from other sources of such as automated path model-following control calculate smooth reference angular velocities signal.Generally, the rate of change of original input signal and higher order derivative are unboundeds.If this original input signal is directly used as the order delivering to driving, then the total of aerial ladder will suffer from high dynamic force, causes big material pressure.Therefore, it is necessary to obtain smooth speed reference signal, it at least has first derivative, i.e. acceleration, but, better, also there is second dervative, i.e. acceleration (jerk), and higher order derivative bounded.In order to obtain acceleration bounded reference signal, it is possible to adopt a second order filter or non linear rate limiter and firstorder filter.Wave filter can be implemented as finite impulse response (FIR) (FIR) wave filter or infinite impulse response (IIR) wave filter.Such wave filter improves system response by reducing acceleration and acceleration, but, only it is only possible to, by the notable response time lengthening system, the excitation significantly reduced particularly the first vibration mode.

In order to improve the elimination to vibration, it is possible to adopt additional vibration to eliminate assembly.For being analogous respectively to (9,10) and (22,23) vibrational system, the method proposing concept based on differential flat degree in " " Flatnessbasedcontrolofoscillators " byRouchon; P.; publishedinZAMM JournalofAppliedMathematicsandMechanics, 85.6 (2005), pp.411 421 ".In the framework of differential flat degree, using so-called virtual " smooth output ", the temporal evolution of the input of system mode (being flexible vibration pattern here) and system is parameterized.Based on the result announced by Rouchon, ignore suppression and respond at fast actuator, i.e. directly speed inputWithHypothesis under, the temporal evolution of the flexible vibration pattern in (10) and (23) is respectively

$f_1^R=\frac{B_2}{{\mathrm{\&omega;}}_1}(\stackrel{\&CenterDot;}{z}+\frac{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{z}}{{\mathrm{\&omega;}}_2^2}),f_2^R=\frac{B_4}{{\mathrm{\&omega;}}_2}(\stackrel{\&CenterDot;}{z}+\frac{\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;\&CenterDot;}{z}}{{\mathrm{\&omega;}}_2^2}).$

Immediately be derivativeWherein, B_iRepresenting i-th row of the corresponding input matrix B in (10) and (23) respectively, z represents the track of " smooth output ".If the time-derivative of track z disappears after certain transit time, then no longer keep residual oscillation.Reference angular velocities required for realizing these tracks is given

$u^{ff}=z+(\frac{1}{{\mathrm{\&omega;}}_1^2}+\frac{1}{{\mathrm{\&omega;}}_2^2})\stackrel{\&CenterDot;\&CenterDot;}{z}+\frac{1}{{\mathrm{\&omega;}}_1^2{\mathrm{\&omega;}}_2^2}\frac{d^{4}z}{{\mathrm{dt}}^4}.$

Therefore, trajectory planning person provide or the reference locus z that obtains from original input signal must be that at least four continuously differentiables divide.For realizing, trajectory planning assembly and vibration suppression assembly can individually realize as previously described, or can be implemented in combination with so that need not calculate reference locus z and derivative thereof clearly.

When vibration suppression assembly is included in feed forward signal path, the state vector restrained in (13) in whole state feedback law (12) and partial state feedback respectively must be replaced by the derivative of the reference locus according to state, such as, for whole feedback of status (12), result is

$u_{fb}=-\left[\begin{array}{cccc}{k}_1^p& k_1^d& k_2^p& k_2^d\end{array}\right](x-{\&lsqb;f_1^R,{\stackrel{\&CenterDot;}{f}}_1^R,f_2^R,{\stackrel{\&CenterDot;}{f}}_2^R\&rsqb;}^t).$

Shown in side view in Fig. 3, the control system of pattern described above device 10 aloft realizes.This aerospace equipment 10 includes telescopic tube 12, and this telescopic tube 12 can whole rotate around vertical axis, and wherein, θ represents the anglec of rotation.Additionally, telescopic tube 12 can with angle of pitch α pitching, and the articulated jib 14 being attached to the end of telescopic tube 14 can relative to telescopic tube 12 with inclination angleTilting, upwardly direction is just defined as.The angular velocity measured by gyroscope is defined as m_T、m_EAnd m_R, it is orthogonal to sleeve pipe and axle in a horizontal plane and in vertical plane, is orthogonal to the axle of sleeve pipe is used separately as the axle of the longitudinal axes parallel with sleeve pipe.Aloft in the preferred embodiment of device 10, gyroscope 16 is located in the fulcrum between the end of telescopic tube 12 and articulated jib 14.

Strain-gage pickup 18 is attached to telescopic tube 12.In this example, these strain-gage pickups (or being abbreviated as SG sensor 18) are closely located to the substrate 20 of aerospace equipment 10.Specifically, four SG sensors 18 are arranged to two pairs.SG sensor in first pair 22 is positioned at the bottom in the cross section of telescopic tube 12, and wherein each transducer arrangements in these a pair 22 is in the side (that is, left side and right side) of telescopic tube 12.SG sensor in second pair 24 is arranged in the push rod of the truss frame of telescopic tube 12 as follows: this each SG sensor of a pair 24 is attached at a side of telescopic tube 12.As a result, in every side of telescopic tube 12, two SG sensors (including a sensor in every pair 22,24 respectively) are attached to above another.If telescopic tube 12 laterally (that is, in the horizontal direction) distortion or bending, then the SG sensor extension difference in every a pair 22,24, because the left horizontal beam in the framework of telescopic tube is different with the extension of right horizontal beam.When the vertical curve of telescopic tube 12, upper beam and the underbeam of framework are same so that the SG sensor 18 of upper and lower extends difference.Specifically, in arranging at this, it is also possible to the twist motion of telescopic tube 12 detected.

Aerospace equipment 10 shown in Fig. 3 also includes controller, and this controller controls the motion of aerospace equipment 10 based on the signal value obtained from SG sensor 18 and gyroscope 16.Represent that above-mentioned model and the control system realized in this controller schematically show in the diagram, and be described below.

Realize this control system shown in Fig. 4, for each axle of aerospace equipment 10.Each control system 50 generally includes feedforward branch circuit 52, feedback branch 54 and drive control signal and calculates branch road 56.In feedforward branch circuit 52, processing as the reference angular velocities value of motion command, this reference angular velocities value from obtaining as the manual lever operated by human operator who or can obtain from such as Trajectory Tracking Control for reproducing previously recorded track, etc..What feedback branch 54 output was computed compensates magnitude of angular velocity to compensate the vibration of aerospace equipment 10, especially compensates the vibration of telescopic tube 12 and articulated jib 14.The consequential signal exported by feedforward branch circuit 52 and feedback branch 54, namely, the feedforward magnitude of angular velocity obtained according to reference angular velocities value and the compensation magnitude of angular velocity of calculating, be all input into drive control signal and calculate the drive control signal that branch road 56 can be used by driving device such as hydraulic drive unit etc. with calculating.

In feedback branch 54, from the primary signal SG that SG sensor 18 and gyroscope 16 obtain_RawAnd GY_RawFor calculating reference signal, this reference signal includes the SG reference signal SG representing strain value and magnitude of angular velocity respectively_RefWith gyroscope reference signal GY_Ref.It addition, also calculate the angular acceleration reference signal AA drawn from angular position value_RefAs reference signal.Reference signal SG_Ref、GY_RefAnd AA_RefBeing input into observer module 58 together with additional model parameter PAR, additional model parameter PAR relates to the structure of aerospace equipment 10, for instance, the length of telescopic tube 12 and articulated jib 14, the current angle of pitch α of telescopic tube 12, the inclination angle of articulated jib 14Deng.Observer module 58 is according to reference signal SG_Ref、GY_RefAnd AA_RefThe first vibration mode f is reconstructed with additional model parameter PAR₁With the second vibration mode f₂, these patterns are input into controlling module 60, for the first vibration mode f according to reconstruct₁With the second vibration mode f₂Calculate compensation magnitude of angular velocity.Compensate magnitude of angular velocity and be output to drive control signal Branch Computed 56 via checking and release module 62.Checking and release realize a logic to determine whether active vibration order is sent to drive control signal branch.

It is more fully described SG reference signal SG below with reference to Fig. 5_RefCalculating, Fig. 5 illustrates SG reference signal Branch Computed 64.In the operating procedure by object number 66 labelling in Figure 5, strain value V_StrainThe primary signal SG of the SG sensor 18 according to the vertical curve measuring telescopic tube_RawMeansigma methods or the primary signal SG of SG sensor 18 according to the horizontal curvature measuring telescopic tube 12 alternatively_RawDifference, calculate according to each spatial axes of considering in calculating at this.Calculating the stress value V for pitching_StrainSituation in, i.e. consider the situation of vertical curve of telescopic tube 12, according at least to the length L of the angle of pitch α of telescopic tube 12, the length L of telescopic tube 12 and articulated jib 14 in operating procedure 17_AA, inclination angle between telescopic tube 12 and articulated jib 14It is attached to the payload in the quality of the cage of the end of articulated jib 14 and this cage to calculate stress biased value V_Off.The strain value V calculated in operating procedure 66_StrainBy deducting the strain-bias value V calculated in operating procedure 71 from this strain value_OffCorrect (operating procedure 70).Particularly being not to be seen as stretching out and retracting or during raising and lowering of oscillating movement at telescopic tube 12, the change to preventing biasing of inserting of strain-bias value is effective.(calibrated) strain value obtained is afterwards as SG reference signal SG_RefFiltered in high pass filter 72 before being input into observer module 58.

High pass filter 72 is single order or higher order high pass filter.The cut-off frequency of this high pass filter is at 20% place of the eigenfrequency of each basic vibration mode.Due to this dependency to eigenfrequency, for the telescopic tube 12 (its first eigenfrequency is higher than greater length of telescopic tube) that length is short, filter effect is enhanced, reason is extending, retract, rise or fall sleeve pipe during, more efficiently carry out filtering of the change to biasing, because can select higher cut-off frequency for longer extension elongation, this shortens the response time of wave filter.

Fig. 6 illustrates the gyroscope reference signal Branch Computed 74 carrying out computing gyroscope reference signal for the gyroscope primary signal according to each axle.In gyroscope reference signal Branch Computed 74, operating procedure 76 calculates the backward difference quotient (backwarddifferencequotient) of angular position measurement signal, to obtain raw velocity estimation signal V_Est, raw velocity estimates signal V_EstAnd then input the low pass filter 78 into the second level.When for the axle of pitching, from the initial primary signal GY of gyroscope_RawDirectly deduct filtered velocity estimation signal V '_Est(operating procedure 82) is to obtain compensated gyroscope signal GY_Cmop, compensated gyroscope signal GY_CompThrough the low pass filter 83 of the first order and as gyroscope reference signal GY_RefOutput.

When rotating axle, it is necessary to obtain angular velocity V '_EstTo a part corresponding to corresponding axis of gyroscope reversed or rotate, it depends on angle of pitch α (operating procedure 80).Afterwards, aforesaid operations 82 is performed, i.e. from the initial primary signal GY of gyroscope_RawDeduct filtered velocity estimation signal V '_EstGained that a part.

Referring again to Fig. 4, in angular acceleration Branch Computed 84, draw angular acceleration reference signal AA by calculating the difference coefficient of the second level from magnitude of angular velocity_Ref, to predict vibration to a certain extent.The angular acceleration reference signal AA obtained_RefIt is also input into observer module 58.It is alternatively possible to angular acceleration reference signal AA_RefFiltering.

In observer module 58, reconstruct the first vibration mode and the temporal evolution of the second vibration mode according to SG reference signal, gyroscope reference signal, angular acceleration reference signal and the additional model parameter relevant to the structure of aerospace equipment 10.This is according to performing with drag.At the length L based on the length L of the sleeve pipe needed for specific ladder model, articulated jib_AA, inclination angle between telescopic tube and articulated jibDuring the operation of the current load in cage, the parameter 85 used in model is stored and is adjusted.

There is the Luenberger observer for pitch axis providing observer state vector in (18) be given by

$\begin{array}{c}\stackrel{\&CenterDot;}{\hat{x}}=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ -{\mathrm{\&omega;}}_1^2& -{\mathrm{\&beta;\&omega;}}_1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& -{\mathrm{\&omega;}}_2^2& -{\mathrm{\&beta;\&omega;}}_2& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]\hat{x}+\left[\begin{array}{c}0\\ b_1\\ 0\\ b_2\\ 0\\ 0\end{array}\right]\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&alpha;}}\\ +L(\left[\begin{array}{c}{\widetilde{\mathrm{\&epsiv;}}}_v\\ {\tilde{m}}_E\end{array}\right]-\left[\begin{array}{cccccc}{c}_1& 0& c_2& 0& 1& 0\\ 0& 1& 0& 1& 0& 1\end{array}\right]\hat{x})\end{array}---\left(25\right)$

In this formula,It is (treated or filtered) SG reference signal of the vertical SG sensor that obtains,It it is the treated He filtered gyroscope reference signal of pitch axis.Remaining side-play amount is modeled as random walk interference and is considered by observer module 58.By adjusting eigenfrequency ω_i, rejection coefficient β, input parameter b_i, output parameter c_iAnd the coefficient of observer matrix L performs the adjustment to different length and angle.In order to reduce the quantity of the coefficient wanting on-line storage and adjustment, it is possible to calculate these coefficients according to by the parameter of the system model (21) of on-line tuning.

The dynamic equation rotating axle is generally identical with pitch axis.Selecting identical state vector (18) for observer, wherein biasing refers to suitable sensor signal.Being similar to equation above, the dynamical equation group of Luenberger observer is given

$\begin{array}{c}\stackrel{\&CenterDot;}{\hat{x}}=\left[\begin{array}{cccccc}0& 1& 0& 0& 0& 0\\ -{\mathrm{\&omega;}}_1^2& -{\mathrm{\&beta;\&omega;}}_1& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& -{\mathrm{\&omega;}}_2^2& -{\mathrm{\&beta;\&omega;}}_2& 0& 0\\ 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0\end{array}\right]\hat{x}+\left[\begin{array}{cc}0& 0\\ g_1^s& g_1^c\\ 0& 0\\ b_2^s& b_2^c\\ 0& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}\sin \mathrm{\&alpha;}\\ cos\mathrm{\&alpha;}\end{array}\right]\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}\\ +L(\left[\begin{array}{c}{\widetilde{\mathrm{\&epsiv;}}}_h\\ {\tilde{m}}_T\end{array}\right]-\left[\begin{array}{cccccc}1& 0& c_2& 0& 1& 0\\ 0& m_1& 0& 1& 0& 1\end{array}\right]\hat{x})\end{array}---\left(26\right)$

In this formula, " strain " coordinate selects first mode and selects the second pattern in " gyroscope " coordinate.For pitch axis, adjust the coefficient of observer gain matrix L for each length and inclination angle, to reconstruct the pattern that noise and interference are carried out fully decay well.Owing to combining bending vibration and twisting vibration, it is possible to select the gain matrix of the reduction for Luenberger observer so that be based only upon strain signal to estimate first mode, obtain the following structure for observer gain matrix:

$L={\left[\begin{array}{cccccc}*& *& *& *& *& *\\ 0& 0& *& *& *& *\end{array}\right]}^t---\left(27\right)$

Wherein, the non-zero record of * representing matrix, and the transposition of subscript t representing matrix.

In alternative realization, it is possible to use from the signal m of axis of gyroscope_R, rather than the signal m of axle_T, in such a case it is necessary to the parameter c properly selected in (26)_iAnd m_i。

Extension elongation L according to sleeve pipe and the length L of articulated jib_AA, and also according to the inclination angle between articulated jib and cage payload, obtain, from predetermined storage location, the model parameter (being represented in Fig. 4) comprised the dynamical equation of Luenberger observer by object 85.

The structure of module 60 is controlled shown in Fig. 7.Control module 60 and generally include Liang Ge branch, i.e. vibration suppression branch 90 (top in Fig. 7) and reference position control branch 92, and vibration suppression branch 90 is used for processing the first vibration mode f₁With the second vibration mode f₂, reference position controls branch 92 and controls component for calculating the reference position that will be explained below.

In vibration suppression branch 90, have employed the first vibration mode f reconstructed by observer module 58₁With the second vibration mode f₂, and these pattern f₁And f₂In each pattern and the factor depending on extension elongation and inclination angleIt is multiplied.After this is multiplied (in operating procedure 94), in operating procedure 96, the signal obtained is added up, to obtain signal value as a result, export this signal value as a result from suppressing branch 90.

Control in reference position in branch 92, calculate current location (being provided by angle of pitch α and rotation angle θ respectively) and deviate from the deviation (in subtracting step 100) of reference position (providing in object 98), to obtain being controlled, by reference position, the reference position control component that branch 92 exports.In additional step 102, reference position control component adds up with both the signal values calculated by vibration suppression branch 90, to obtain being exported compensation magnitude of angular velocity by controlling module 60.

As shown in Figure 4, in drive control signal Branch Computed 56, the magnitude of angular velocity that compensates obtained is added with the feedforward magnitude of angular velocity exported by feed forward branch 52, to calculate drive control signal (position 106).

In feed forward branch 52, the original input signal etc. obtained from manual input equipment is input into trajectory planning assembly 51.The reference angular velocities signal exported by trajectory planning assembly 51 is eliminated assembly 53 by dynamic vibration below and revises, and to reduce the excitation to vibration, dynamic vibration eliminates assembly 53 output feedforward magnitude of angular velocity.

Claims (12)

1. the method for controlling aerospace equipment,

Described aerospace equipment includes:

-telescopic tube (12),

-strain-gage pickup (18), described strain-gage pickup (18) is used for detecting described telescopic tube (12) case of bending in the horizontal direction and the vertical direction,

-gyroscope (16), described gyroscope (16) is attached to the top of described telescopic tube (12), and

-controlling equipment, described control equipment controls the motion of described aerospace equipment based on the signal value obtained from described strain-gage pickup and described gyroscope,

Described method comprises the following steps:

-obtain primary signal SG from described strain-gage pickup (18) and described gyroscope (16)_RawAnd GY_Raw,

-according to described primary signal SG_RawAnd GY_RawCalculating reference signal, described reference signal includes the strain gauge reference signal SG representing strain value_RefWith the gyroscope reference signal GY representing magnitude of angular velocity_Ref, and calculate the angular acceleration reference signal AA being worth going out from angular position value or angular velocity measurement_Ref,

-reconstruct the first vibration mode f according to described reference signal and the additional model parameter PAR relevant with the structure of described aerospace equipment₁With than described first vibration mode f₁At least one of higher order the second vibration mode f₂,

-according to the first vibration mode f reconstructed₁With at least one the second vibration mode f₂Calculate compensation magnitude of angular velocity AV_Comp,

-by computed compensation magnitude of angular velocity AV_CompIt is added to obtain drive control signal with feedforward magnitude of angular velocity.

2. method according to claim 1, it is characterised in that calculate strain gauge reference signal SG_RefIncluding:

The described primary signal SG of the strain-gage pickup (18) according to the vertical curve measuring described telescopic tube_RawMeansigma methods or measure the described primary signal SG of strain-gage pickup (18) of horizontal curvature of described telescopic tube (12)_RawDifference calculate strain value V_Strain,

-to described strain value V_StrainCarry out high-pass filtering.

3. method according to claim 2, it is characterised in that calculate described strain gauge reference signal SG_RefIncluding:

-insert described strain-bias value V according to the angle of pitch of described telescopic tube (12) and the extension elongation of described telescopic tube (12)_Off,

-pass through before high-pass filtering from described strain value V_StrainDeduct described strain-bias value V_OffCorrect described strain value V_Strain。

4. method according to claim 3, it is characterised in that insert described strain-bias value V_OffIt is additionally based upon the extension elongation of the articulated jib (14) of the end being attached to described telescopic tube (12) and the inclination angle between described telescopic tube (12) and described articulated jib (14).

5. require the method described in 3 or 4 according to claims, it is characterised in that insert described strain-bias value V_OffIt is additionally based upon the end being attached to described telescopic tube (12) or is attached to the load in the quality of cage of end of described articulated jib (14) and described cage.

6. method as claimed in any of claims 1 to 4, it is characterised in that calculate described gyroscope reference signal GY_RefIncluding:

-calculate described primary signal GY according to angular position measurement value_RawBackward difference quotient to obtain Attitude rate estimator signal V_Est,

-by low pass filter to described Attitude rate estimator signal V_EstIt is filtered,

-calculate the filtered described Attitude rate estimator signal V ' being associated with each axle of described gyroscope_EstParticular,

-from the initial described primary signal GY from described gyroscope (16)_RawDeduct filtered described Attitude rate estimator signal V '_EstThis part, to obtain compensated gyroscope signal GY_Comp,

-to compensated gyroscope signal GY_CompCarry out low-pass filtering.

7. the method according to any one in claims requirement 1 to 4, it is characterised in that calculate described compensation magnitude of angular velocity AV_CompComponent is controlled and according to the first reconstructed vibration mode f including reference position₁With at least one the second vibration mode f₂The signal value calculated is added, and described reference position control component relates to current location and deviates from the deviation of reference position.

8. method as claimed in any of claims 1 to 4, it is characterized in that, described feedforward magnitude of angular velocity obtains from the trajectory planning assembly (51) calculating reference angular velocities signal based on original input signal, and dynamic vibration eliminates assembly (53) and revises described reference angular velocities signal to reduce the excitation to vibration.

9. an aerospace equipment, including:

Telescopic tube (12),

Strain-gage pickup (18), described strain-gage pickup (18) is used for detecting described telescopic tube (12) case of bending in the horizontal direction and the vertical direction,

Gyroscope (16), described gyroscope (16) is attached to the top of described telescopic tube (12), and

Control equipment, described control equipment controls the motion of described aerospace equipment based on the signal value obtained from described strain-gage pickup (18) and described gyroscope (16),

Wherein, described control equipment realizes the control method according to any one in aforementioned claim.

10. aerospace equipment according to claim 9, it is characterized in that, at least four strain-gage pickup (18) is with two pairs (22,24) arrange, it is arranged in top and the lower curtate of the cross section of described telescopic tube (12) for every a pair, makes two strain-gage pickups of every centering be arranged in the opposite side of described telescopic tube (12).

11. the aerospace equipment according to claim 9 or 10, it is characterised in that described aerospace equipment also includes the articulated jib (14) being attached to the end of described telescopic tube (12).

12. the aerospace equipment according to claim 9 or 10, it is characterised in that the rescue cage of end that described aerospace equipment also includes being attached to described telescopic tube (12) or the end that is attached to described articulated jib (14).